Khan Academy on a Stick : Functions and their graphs

Khan Academy on a Stick

Trigonometry and precalculus

What is a function
Function example problems
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Linear Function Graphs
Ex: Constructing a function
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Basic Linear Function
Functions Part 2
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More examples of solving function problems
Functions as Graphs
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Functions (Part III)
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Even more examples of function exercises. Introduction of a graph as definition of a function.
Functions (part 4)
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An example of a functions problem submitted by a youtube viewer
Sum of Functions
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Sum of Functions
Difference of Functions
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Difference of Functions
Product of Functions
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Product of Functions
Quotient of Functions
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Quotient of functions and factoring by grouping
Domain of a function
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Figuring out the domain of a function

Introduction to functions

You've already been using functions in algebra, but just didn't realize it. Now you will. By introducing a little more notation and a few new ideas, you'll hopefully realize that functions are a very, very powerful tool. This tutorial is an old one that Sal made in the early days of Khan Academy. It is rough on the edges (and in between the edges), but it does go through the basic idea of what a function is and how we can define and evaluate functions.

Domain of a function
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Figuring out the domain of a function
Domain and Range of a Relation
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Domain and Range of a Relation
Domain and Range of a Function Given a Formula
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Domain and Range of a Function Given a Formula
Domain and Range 1
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Domain and Range 1
Domain of a Radical Function
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Domain of a Radical Function
Domain and Range 2
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Domain and Range 2
Domain and Range of a Function
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Domain and range

What values can you and can you not input into a function? What values can the function output? The domain is the set of values that the function is defined for (i.e., the values that you can input into a function). The range is the set of values that the function output can take on. This tutorial covers the ideas of domain and range through multiple worked examples. These are really important ideas as you study higher mathematics.

Introduction to Function Inverses
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Introduction to Function Inverses
Function Inverse Example 1
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Function Inverse Example 1
Function Inverses Example 2
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Function Inverses Example 2
Function Inverses Example 3
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Function Inverses Example 3

Function inverses

Functions associate a set of inputs with a set of outputs (in fancy language, they "map" one set to another). But can we go the other way around? Are there functions that can start with the outputs as inputs and produce the original inputs as outputs? Yes, there are! They are called function inverses! This tutorial works through a bunch of examples to get you familiar with the world of function inverses.

Recognizing odd and even functions
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Even and odd functions
Connection between even and odd numbers and functions
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A possible reason why even functions are called "even" and odd functions are called "odd"
Shifting and reflecting functions
Shifting functions
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Graphs of Square Root Functions
Recognizing features of functions 2 (example 2)
Recognizing features of functions 2 (example 3)
Comparing features of functions 2 (example 1)
Comparing features of functions 2 (example 2)

Analyzing functions

You know a function when you see one, but are curious to start looking deeper at their properties. Some functions seem to be mirror images around the y-axis while others seems to be flipped mirror images while others are neither. How can we shift and reflect them? This tutorial addresses these questions by covering even and odd functions. It also covers how we can shift and reflect them. Enjoy!

Why Dividing by Zero is Undefined
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Thinking about why dividing by zero is left undefined
Why Zero Divided by Zero is Undefined/Indeterminate
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Multiple arguments for what we could get when we divide zero by zero. We will later see that this can be considered indeterminate
Undefined and Indeterminate
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Why 0/0 is considered to be indeterminate

Undefined and indeterminate answers

In second grade you may have raised your hand in class and asked what you get when you divide by zero. The answer was probably "it's not defined." In this tutorial we'll explore what that (and "indeterminate") means and why the math world has left this gap in arithmetic. (They could define something divided by 0 as 7 or 9 or 119.57 but have decided not to.)

A more formal understanding of functions
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A more formal understanding of functions
Introduction to the inverse of a function
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Introduction to the inverse of a function

More mathy functions

In this tutorial, we'll start to use and define functions in more "mathy" or formal ways.